Question

The formula for the sum of an infinite geometric series, S = StartFraction a 1 Over 1 minus r EndFraction, may be used to convert 0. ModifyingAbove 2 3 with bar to a fraction. What are the values of a 1 and r? a 1 = StartFraction 23 Over 10 EndFraction, r = one-tenth a 1 = 23, r = StartFraction 1 Over 100 EndFraction a 1 = StartFraction 23 Over 100 EndFraction, r = 100 a 1 = StartFraction 23 Over 100 EndFraction, r = StartFraction 1 Over 100 EndFraction.

Answer 1

The value of a1  is 0.23 and the value of r is 1/100 and this can be determined by using the concept of Geometric progression.

Given :

• The formula for the sum of an infinite geometric series,$\rm s= \dfrac{a1}{1-r}$ .

• Fraction 0.23 (Repeated)

The following steps can be used in order to determine the values of a1 and r:

• Step 1 - The given repeated fraction can be written as:

                    0.2323232323... = 0.23 + 0.0023 + 0.000023 +...

• Step 2 - The above series is in geometric progression.

• Step 3 - So, the value of a1 is 0.23.

• Step 4 - The value of the geometric ratio can be calculated as:

                    $\rm r= \dfrac{0.0023}{0.23}\\ \\ r=\dfrac{1}{100}$

Therefore, The value of a1 is 0.23 and the value of r is 1/100.

Learn more about Geometric progression here :  https://brainly.com/question/14320920